Finite Group Databasebeta

← C2×#23775513 #35164861

Subgroups — C2×#23775513 #35164861

Order 20224.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099270C211yesmaximal, characteristic, complemented
2C2×#19099222C211yesmaximal, characteristic
3#23775513C2116yesmaximal, direct product factor
4C2×#19098923C211yesmaximal, characteristic, complemented
5C2×#19098882C211yesmaximal, characteristic, complemented
6C2×#19098894C211yesmaximal, characteristic, complemented
7C2×#19098849C211yesmaximal, characteristic, complemented
8C2×#19098821C211yesmaximal, characteristic, complemented
9C2×#19098792C211yesmaximal, characteristic, complemented
10C2×#19098786C211yesmaximal, characteristic, complemented
11C2×#19098727C211yesmaximal, characteristic, complemented
12C2×#19098721C211yesmaximal, characteristic, complemented
13C2×#19098671C211yesmaximal, characteristic, complemented
14C2×#19098565C211yesmaximal, characteristic, complemented
15C22×#14579086C211yesmaximal, characteristic, complemented
16C2×#435×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C23×Dic158C2211yescharacteristic
19C22×Dic316C2211yescharacteristic
20C22×Dic316C2211yescharacteristic
21C22×#11929613C2211yescharacteristic
22#19099270—24no—
23#19099270C2218yescomplemented
24#19099222—24no—
25#19099222C2218yes—
26C2×#14579161C2211yescharacteristic
27C2×#14579152—21no—
28C2×#14579149C2211yescharacteristic
29C2×#14579147—21no—
30C2×#14579140C2211yescharacteristic
31C2×#14579140C2211yescharacteristic
32C2×#14579140C2211yescharacteristic
33C2×#14579139—21no—
34C2×#14579138—21no—
35C2×#14579138—21no—
36C2×#14579135C2211yescharacteristic
37C2×#14579133—21no—
38C2×C4×Dic158C2211yescharacteristic
39C2×C4×Dic158C2211yescharacteristic
40C2×D4×Dic79—21no—
41C2×(C22⋊D79)⋊C4—21no—
42C22×C4⋊Dic79C2211yescharacteristic
43C22×C4⋊Dic79C2211yescharacteristic
44#19098923C2218yescomplemented
45#19098894C2218yescomplemented
46#19098882C2218yescomplemented
47#19098849C2218yescomplemented
48#19098821C2218yescomplemented
49#19098792C2218yescomplemented
50#19098786C2218yescomplemented
51#19098727C2218yescomplemented
52#19098721C2218yescomplemented
53#19098671C2218yescomplemented
54C2×#14579093C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57#19098565C2218yescomplemented
58C2×#14579086C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579086C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579086C2218yescomplemented
66C2×#14579083C2211yescharacteristic
67C2×#14579083C2211yescharacteristic
68C2×#14579083C2211yescharacteristic
69C22×M16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#435×C79C2218yescomplemented
73C2×C4⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×C22⋊C8×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C2×#11929624—22no—
78C2×#11929624—24no—
79C2×#11929624—42no—
80C2×#11929624C2314yes—
81C22×Dic158—22no—
82C22×Dic158—21no—
83C22×Dic158—21no—
84C22×Dic158—24no—
85C22×Dic158—42no—
86C22×Dic158C2311yescharacteristic
87C22×Dic158C2311yescharacteristic
88C22×Dic158C2314yes—
89C22×Dic158C2311yescharacteristic
90C22×D316C2311yescharacteristic
91C22×C22⋊D79—21no—
92C22×C22⋊D79—21no—
93C23×Dic79—21no—
94C23×Dic79—21no—
95C23×Dic79—21no—
96C22×C4×D79—21no—
97C2×Dic316—24no—
98C2×Dic316—42no—
99C2×Dic316C2314yes—
100C2×Dic316C2314yes—
101C2×#11929613—42no—
102C2×#11929613C2314yes—
103#14579161—22no—
104#14579161C2314yes—
105#14579152—28no—
106#14579149—22no—
107#14579149C2314yes—
108#14579147—28no—
109#14579140—22no—
110#14579140—22no—
111#14579140—22no—
112#14579140C2314yes—
113#14579140C2314yes—
114#14579140C2314yes—
115#14579139—28no—
116#14579138—28no—
117#14579138—28no—
118#14579135—22no—
119#14579135C2314yes—
120#14579133—28no—
121C4×Dic158—22no—
122C4×Dic158—22no—
123C4×Dic158C2314yes—
124C4×Dic158C2314yes—
125D4×Dic79—28no—
126(C22⋊D79)⋊C4—28no—
127C2×C4⋊Dic79—22no—
128C2×C4⋊Dic79—22no—
129C2×C4⋊Dic79—21no—
130C2×C4⋊Dic79—21no—
131C2×C4⋊Dic79—21no—
132C2×C4⋊Dic79C2314yes—
133C2×C4⋊Dic79C2314yes—
134C2×C4⋊Dic79C2311yescharacteristic
135C2×C4⋊Dic79C2311yescharacteristic
136C2×C4⋊Dic79C2311yescharacteristic
137C2×C4⋊Dic79C2311yescharacteristic
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4—21no—
140C2×Dic79⋊C4—21no—
141C2×Dic79⋊C4—21no—
142C2×Dic79⋊C4—21no—
143C2×C22⋊Dic79—21no—
144C2×C22⋊Dic79—21no—
145C2×C22⋊Dic79—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×(C2×D79)⋊C4—21no—
148C2×(C2×D79)⋊C4—21no—
149C2×C4×Dic79—21no—
150C2×C4×Dic79—21no—
151#14579093C2314yes—
152#14579093C2314yes—
153#14579093C2314yes—
154#14579086C2314yes—
155#14579086C2314yes—
156#14579086C2314yes—
157#14579086C2314yes—
158#14579086C2314yes—
159#14579086C2314yes—
160#14579086C2314yes—
161#14579083C2314yes—
162#14579083C2314yes—
163#14579083C2314yes—
164C22×D4×C79D411yescharacteristic
165C23×C4×C79C2311yescharacteristic
166C23×C4×C79C2311yescharacteristic
167C2×M16×C79—42no—
168C2×M16×C79C2314yes—
169C22×C8×C79—42no—
170C22×C8×C79C2311yescharacteristic
171C22×C8×C79C2311yescharacteristic
172C22×C8×C79C2311yescharacteristic
173C22×C8×C79C2311yescharacteristic
174C22×C8×C79C2314yes—
175C4×D4×C79D414yes—
176C4×D4×C79C2314yes—
177C2×C4⋊C4×C79D411yescharacteristic
178C2×C22⋊C4×C79D411yescharacteristic
179C2×C22⋊C4×C79D411yescharacteristic
180C2×C42×C79C2311yescharacteristic
181C4⋊C8×C79C2314yes—
182C22⋊C8×C79C2314yes—
183C22⋊C8×C79C2314yes—
184#97×C79C2314yes—
185C23×D79—21no—
186#11929624—28no—
187#11929624—44no—
188#11929624—48no—
189C2×Dic158—28no—
190C2×Dic158—21no—
191C2×Dic158—24no—
192C2×Dic158—21no—
193C2×Dic158—21no—
194C2×Dic158—24no—
195C2×Dic158—22no—
196C2×Dic158—22no—
197C2×Dic158—22no—
198C2×Dic158—22no—
199C2×Dic158—22no—
200C2×Dic158—44no—
201C2×Dic158—48no—
202C2×Dic158—44no—
203C2×Dic158—82no—
204C2×Dic158#4114yes—
205C2×Dic158C2412yes—
206C2×Dic158C2412yes—
207C2×Dic158C2412yes—
208C2×D316—21no—
209C2×D316—22no—
210C2×D316—22no—
211C2×D316C2412yes—
212C2×C22⋊D79—24no—
213C2×C22⋊D79—24no—
214C2×C22⋊D79—44no—
215C2×C22⋊D79—44no—
216C22×Dic79—21no—
217C22×Dic79—21no—
218C22×Dic79—24no—
219C22×Dic79—21no—
220C22×Dic79—21no—
221C22×Dic79—21no—
222C22×Dic79—21no—
223C22×Dic79—21no—
224C22×Dic79—24no—
225C22×Dic79—24no—
226C22×Dic79—44no—
227C22×Dic79—82no—
228C22×Dic79—82no—
229C2×C4×D79—24no—
230C2×C4×D79—44no—
231Dic316—28no—
232Dic316—44no—
233#11929613—44no—
234C4⋊Dic79—21no—
235C4⋊Dic79—24no—
236C4⋊Dic79—24no—
237C4⋊Dic79—21no—
238C4⋊Dic79—21no—
239C4⋊Dic79—24no—
240C4⋊Dic79—21no—
241C4⋊Dic79C2412yes—
242C4⋊Dic79C2412yes—
243C4⋊Dic79C2412yes—
244C4⋊Dic79C2412yes—
245Dic79⋊C4—24no—
246Dic79⋊C4—24no—
247Dic79⋊C4—24no—
248Dic79⋊C4—24no—
249Dic79⋊C4—24no—
250C22⋊Dic79—24no—
251C22⋊Dic79—24no—
252C22⋊Dic79—24no—
253(C2×D79)⋊C4—24no—
254(C2×D79)⋊C4—24no—
255(C2×D79)⋊C4—24no—
256C4×Dic79—24no—
257C4×Dic79—24no—
258C24×C79C2×D411yescharacteristic
259C24×C79C2×D411yescharacteristic
260C2×D4×C79—24no—
261C2×D4×C79C2×D414yes—
262C22×C4×C79—22no—
263C22×C4×C79—22no—
264C22×C4×C79—22no—
265C22×C4×C79—22no—
266C22×C4×C79C2×D411yescharacteristic
267C22×C4×C79C2×D411yescharacteristic
268C22×C4×C79C2×D412yes—
269C22×C4×C79C2×D412yes—
270C22×C4×C79C2×D411yescharacteristic
271C22×C4×C79C2×D411yescharacteristic
272C22×C4×C79C2412yes—
273C22×C4×C79C2412yes—
274C22×C4×C79C2411yescharacteristic
275M16×C79—44no—
276C2×C8×C79—22no—
277C2×C8×C79—22no—
278C2×C8×C79—22no—
279C2×C8×C79—22no—
280C2×C8×C79—44no—
281C2×C8×C79C2412yes—
282C2×C8×C79C2412yes—
283C2×C8×C79C2412yes—
284C2×C8×C79C2412yes—
285C4⋊C4×C79C2×D414yes—
286C22⋊C4×C79C2×D414yes—
287C22⋊C4×C79C2×D414yes—
288C42×C79C2×D412yes—
289C42×C79C2412yes—
290C23×C79—22no—
291C23×C79—22no—
292C23×C79—22no—
293C23×C79—22no—
294C23×C79—22no—
295C23×C79#13714yes—
296C23×C79C22×D412yes—
297C23×C79C22×D412yes—
298C23×C79C22×D411yescharacteristic
299C22×D79—22no—
300C22×D79—42no—
301C22×D79—42no—
302C22×D79—42no—
303D4×C79—28no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—24no—
309C2×C4×C79—24no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79C22×D412yes—
315C2×C4×C79C22×D412yes—
316C2×C4×C79C22×D412yes—
317C2×C4×C79C22×D412yes—
318C2×C4×C79C22×D411yescharacteristic
319C2×C4×C79C2×#4112yes—
320C2×C4×C79H(5,𝔽2)12yes—
321C2×C4×C79C2511yescharacteristic
322C22⋊D79—48no—
323C22⋊D79—48no—
324C2×Dic79—24no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—22no—
332C2×Dic79—48no—
333C2×Dic79—42no—
334C2×Dic79—42no—
335C2×Dic79—42no—
336C2×Dic79—42no—
337C2×Dic79—42no—
338C2×Dic79—42no—
339C2×Dic79—84no—
340C2×Dic79—84no—
341D316—22no—
342D316—22no—
343D316—42no—
344C4×D79—48no—
345Dic158—24no—
346Dic158—22no—
347Dic158—22no—
348Dic158—22no—
349Dic158—22no—
350Dic158—22no—
351Dic158—48no—
352Dic158—42no—
353Dic158—42no—
354Dic158—84no—
355Dic158C2×#4114yes—
356C8×C79—22no—
357C8×C79—22no—
358C8×C79—22no—
359C8×C79—22no—
360C22×C79—22no—
361C22×C79—28no—
362C22×C79—22no—
363C22×C79—22no—
364C22×C79—22no—
365C22×C79—22no—
366C22×C79—44no—
367C22×C79#54612yes—
368C22×C79C2×#13714yes—
369C22×C79C2×#13712yes—
370C22×C79#57712yes—
371C22×C79C23×D411yescharacteristic
372C2×D79—42no—
373C2×D79—42no—
374C2×D79—42no—
375C2×D79—84no—
376C4×C79—22no—
377C4×C79—22no—
378C4×C79—22no—
379C4×C79—22no—
380C4×C79#54612yes—
381C4×C79C22×#4111yescharacteristic
382C4×C79C2×H(5,𝔽2)11yescharacteristic
383Dic79—24no—
384Dic79—42no—
385Dic79—42no—
386Dic79—42no—
387Dic79—42no—
388Dic79—42no—
389Dic79—42no—
390C2×#3316—791nomaximal, Sylow
391C2×C79—24no—
392C2×C79—42no—
393C2×C79#331614yescomplemented
394C2×C79C2×#54611yescharacteristic
395C2×C79C22×#13711yescharacteristic
396C2×C79C2×#57711yescharacteristic
397D79—82no—
398C2×#554—791no—
399C2×#548—791no—
400#3316—7916no—
401C2×#489—791no—
402C2×#481—791no—
403C2×#483—791no—
404C2×#475—791no—
405C2×#470—791no—
406C2×#465—791no—
407C2×#464—791no—
408C2×#452—791no—
409C2×#451—791no—
410C2×#441—791no—
411C2×#435D7911yescharacteristic, complemented
412C2×#417—791no—
413C22×#103—791no—
414C79C2×#331611yescharacteristic, complemented, Sylow
415C22×#41—791no—
416C23×Q8—791no—
417C22×Q16—791no—
418C22×Q16—791no—
419C22×SD16—791no—
420C22×M16C2×D7911yescharacteristic
421C23×C8C2×D7911yescharacteristic
422#554—798no—
423#554—1584no—
424#548—798no—
425#548—1584no—
426C2×C4⋊Q8—791no—
427C2×#125—1581no—
428C2×#124—791no—
429C2×#124—1581no—
430C2×C22⋊Q8—791no—
431C2×C22⋊Q8—791no—
432C2×C22⋊Q8—791no—
433C2×C22⋊Q8—1581no—
434C2×C22⋊Q8—1581no—
435C2×C22⋊Q8—1581no—
436C2×#121—791no—
437C2×#121—1581no—
438C2×C4×Q8—791no—
439C2×C4×Q8—791no—
440C2×C4×D4—1581no—
441C2×C4×D4—1581no—
442C2×C4×D4C2×D7911yescharacteristic
443C22×C4⋊C4—791no—
444C22×C4⋊C4—791no—
445#489—798no—
446#483—798no—
447#481—798no—
448#475—798no—
449#470—798no—
450#465—798no—
451#464—798no—
452#452—798no—
453#451—798no—
454#441—798no—
455#435C2×D7918yescomplemented
456C2×#106—791no—
457C2×#106—791no—
458C2×#106—791no—
459C2×C4⋊C8C2×D7911yescharacteristic
460#417—798no—
461C2×#103—791no—
462C2×#103—791no—
463C2×#103—791no—
464C2×#103—791no—
465C2×#103—791no—
466C2×#103—791no—
467C2×#103—798no—
468C2×#103—791no—
469C2×#102—791no—
470C2×#102—791no—
471C2×#102—791no—
472C2×C22⋊C8C2×D7911yescharacteristic
473C2×C22⋊C8C2×D7911yescharacteristic
474C2×#97C2×D7911yescharacteristic
475C2×#41—3162no—
476C2×#41—794no—
477C2×#41—1584no—
478C2×#41—1582no—
479C22×Q8—3162no—
480C22×Q8—794no—
481C22×Q8—791no—
482C22×Q8—791no—
483C22×Q8—791no—
484C22×Q8—1584no—
485C22×Q8—1581no—
486C22×Q8—1582no—
487C22×Q8—1581no—
488C22×D4—791no—
489C22×D4—1581no—
490C22×D4—1581no—
491C22×D4D31611yescharacteristic
492C23×C4—1581no—
493C23×C4—1581no—
494C23×C4—1581no—
495C23×C4—1581no—
496C23×C4C22×D7911yescharacteristic
497C23×C4C22×D7911yescharacteristic
498C2×Q16—3162no—
499C2×Q16—794no—
500C2×Q16—794no—
501C2×Q16—1584no—
502C2×SD16—3162no—
503C2×SD16—794no—
504C2×M16—42no—
505C2×M16C22×D7914yes—
506C22×C8—42no—
507C22×C8C22×D7911yescharacteristic
508C22×C8C22×D7911yescharacteristic
509C22×C8C22×D7911yescharacteristic
510C22×C8C22×D7911yescharacteristic
511C22×C8C22×D7914yes—
512C4⋊Q8—794no—
513C4⋊Q8—1582no—
514#125—1588no—
515#124—794no—
516#124—1588no—
517#124—1582no—
518C22⋊Q8—794no—
519C22⋊Q8—794no—
520C22⋊Q8—794no—
521C22⋊Q8—1582no—
522C22⋊Q8—1582no—
523C22⋊Q8—1582no—
524C22⋊Q8—1588no—
525C22⋊Q8—1588no—
526C22⋊Q8—1588no—
527#121—794no—
528#121—1588no—
529#121—1582no—
530C4×Q8—794no—
531C4×Q8—794no—
532C4×Q8—1582no—
533C4×Q8—1582no—
534C4×D4—1588no—
535C4×D4—1588no—
536C4×D4D31614yes—
537C4×D4C22×D7914yes—
538C2×C4⋊C4—791no—
539C2×C4⋊C4—791no—
540C2×C4⋊C4—791no—
541C2×C4⋊C4—794no—
542C2×C4⋊C4—794no—
543C2×C4⋊C4—791no—
544C2×C4⋊C4—1581no—
545C2×C4⋊C4—1581no—
546C2×C4⋊C4—1582no—
547C2×C4⋊C4—1582no—
548C2×C4⋊C4—1581no—
549C2×C4⋊C4—1581no—
550C2×C4⋊C4—1581no—
551C2×C4⋊C4—1581no—
552C2×C4⋊C4—1581no—
553C2×C4⋊C4—1581no—
554C2×C4⋊C4D31611yescharacteristic
555C2×C22⋊C4—1581no—
556C2×C22⋊C4—1581no—
557C2×C22⋊C4—1581no—
558C2×C22⋊C4—1581no—
559C2×C22⋊C4—1581no—
560C2×C22⋊C4—1581no—
561C2×C22⋊C4D31611yescharacteristic
562C2×C22⋊C4D31611yescharacteristic
563C2×C42—1581no—
564C2×C42—1581no—
565C2×C42C22×D7911yescharacteristic
566#106—794no—
567#106—794no—
568#106—794no—
569C4⋊C8C22×D7914yes—
570#103—794no—
571#103—794no—
572#103—794no—
573#103—794no—
574#103—794no—
575#103—794no—
576#103—794no—
577#102—794no—
578#102—794no—
579#102—794no—
580C22⋊C8C22×D7914yes—
581C22⋊C8C22×D7914yes—
582#97C22×D7914yes—
583C24—1581no—
584C24C2×D31611yescharacteristic
585C24C2×D31611yescharacteristic
586#41—3168no—
587#41—3164no—
588#41—1588no—
589C2×Q8—3168no—
590C2×Q8—3164no—
591C2×Q8—3164no—
592C2×Q8—794no—
593C2×Q8—792no—
594C2×Q8—792no—
595C2×Q8—792no—
596C2×Q8—6322no—
597C2×Q8—1588no—
598C2×Q8—1582no—
599C2×Q8—1582no—
600C2×Q8—1582no—
601C2×Q8—1582no—
602C2×Q8—1582no—
603C2×Q8—1581no—
604C2×Q8—1581no—
605C2×Q8—1584no—
606C2×Q8—1584no—
607C2×Q8—1581no—
608C2×D4—24no—
609C2×D4—3164no—
610C2×D4—3164no—
611C2×D4—792no—
612C2×D4—1584no—
613C2×D4—1584no—
614C2×D4—1582no—
615C2×D4—1582no—
616C2×D4—1581no—
617C2×D4C2×D31614yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—3164no—
623C22×C4—3164no—
624C22×C4—6322no—
625C22×C4—6322no—
626C22×C4—1584no—
627C22×C4—1581no—
628C22×C4—1581no—
629C22×C4—1581no—
630C22×C4—1581no—
631C22×C4—1581no—
632C22×C4—1581no—
633C22×C4—1584no—
634C22×C4—1584no—
635C22×C4—1584no—
636C22×C4—1581no—
637C22×C4C2×D31612yes—
638C22×C4C2×D31612yes—
639C22×C4C2×D31611yescharacteristic
640C22×C4C2×D31611yescharacteristic
641C22×C4C2×D31611yescharacteristic
642C22×C4C2×D31611yescharacteristic
643C22×C4C23×D7912yes—
644C22×C4C23×D7912yes—
645C22×C4C23×D7911yescharacteristic
646Q16—3164no—
647Q16—1588no—
648SD16—3164no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—44no—
655C2×C8C23×D7912yes—
656C2×C8C23×D7912yes—
657C2×C8C23×D7912yes—
658C2×C8C23×D7912yes—
659C4⋊C4—792no—
660C4⋊C4—792no—
661C4⋊C4—792no—
662C4⋊C4—792no—
663C4⋊C4—1584no—
664C4⋊C4—1584no—
665C4⋊C4—1584no—
666C4⋊C4—1584no—
667C4⋊C4—1584no—
668C4⋊C4—1581no—
669C4⋊C4—1584no—
670C4⋊C4—1584no—
671C4⋊C4—1581no—
672C4⋊C4—1581no—
673C4⋊C4—1581no—
674C4⋊C4—1584no—
675C4⋊C4C2×D31614yes—
676C22⋊C4—1584no—
677C22⋊C4—1584no—
678C22⋊C4—1584no—
679C22⋊C4—1584no—
680C22⋊C4—1584no—
681C22⋊C4—1584no—
682C22⋊C4C2×D31614yes—
683C22⋊C4C2×D31614yes—
684C42—1584no—
685C42—1584no—
686C42C2×D31612yes—
687C42C23×D7912yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—3162no—
694C23—3162no—
695C23—3162no—
696C23—1582no—
697C23#1457919414yes—
698C23C22×D31612yes—
699C23C22×D31612yes—
700C23C22×D31611yescharacteristic
701Q8—3168no—
702Q8—3162no—
703Q8—3162no—
704Q8—794no—
705Q8—6324no—
706Q8—1582no—
707Q8—1582no—
708Q8—1582no—
709Q8—1582no—
710Q8—1582no—
711Q8—1584no—
712D4—28no—
713D4—3168no—
714D4—3168no—
715D4—3162no—
716D4—1582no—
717D4—1582no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—3168no—
729C2×C4—3162no—
730C2×C4—3162no—
731C2×C4—3162no—
732C2×C4—3162no—
733C2×C4—3162no—
734C2×C4—3162no—
735C2×C4—3168no—
736C2×C4—6324no—
737C2×C4—6324no—
738C2×C4—1582no—
739C2×C4—1582no—
740C2×C4—1582no—
741C2×C4—1582no—
742C2×C4—1582no—
743C2×C4—1582no—
744C2×C4—1584no—
745C2×C4—1582no—
746C2×C4C22×D31612yes—
747C2×C4C22×D31612yes—
748C2×C4C22×D31612yes—
749C2×C4C22×D31612yes—
750C2×C4C22×D31611yescharacteristic
751C2×C4#41×D7912yes—
752C2×C4#1457920612yes—
753C2×C4C24×D7911yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—3162no—
766C22—3162no—
767C22—3162no—
768C22—6324no—
769C22#1909920812yes—
770C22C2×#1457919414yes—
771C22C2×#1457919412yes—
772C22#1909937512yes—
773C22C23×D31611yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—3162no—
779C4—3162no—
780C4—3162no—
781C4—3162no—
782C4—3162no—
783C4—3162no—
784C4—1584no—
785C4#1909920812yes—
786C4C2×#41×D7911yescharacteristic
787C4C2×#1457920611yescharacteristic
788C2—24no—
789C2—42no—
790C2—6322no—
791C2#2377551314yesdirect product factor
792C2C2×#1909920811yescharacteristic
793C2C22×#1457919411yescharacteristic
794C2C2×#1909937511yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#435×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099222C2
hypercenterC2×#435D79
hypocenterC79C2×#3316
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19099270C2semidirect
3. #23775513C2direct (N × H)
4. C2×#19098923C2semidirect
5. C2×#19098882C2semidirect
6. C2×#19098894C2semidirect
7. C2×#19098849C2semidirect
8. C2×#19098821C2semidirect
9. C2×#19098792C2semidirect
10. C2×#19098786C2semidirect
11. C2×#19098727C2semidirect
12. C2×#19098721C2semidirect
13. C2×#19098671C2semidirect
14. C2×#19098565C2semidirect
15. C22×#14579086C2semidirect
16. C2×#435×C79C2semidirect
23. #19099270C22semidirect
44. #19098923C22semidirect
45. #19098894C22semidirect
46. #19098882C22semidirect
47. #19098849C22semidirect
48. #19098821C22semidirect
49. #19098792C22semidirect
50. #19098786C22semidirect
51. #19098727C22semidirect
52. #19098721C22semidirect
53. #19098671C22semidirect
57. #19098565C22semidirect
65. C2×#14579086C22semidirect
72. #435×C79C22semidirect
393. C2×C79#3316semidirect
411. C2×#435D79semidirect
414. C79C2×#3316semidirect
455. #435C2×D79semidirect
791. C2#23775513direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#190992702
C2×#190992222
#237755132
C2×#190989232
C2×#190988822
C2×#190988942
C2×#190988492
C2×#190988212
C2×#190987922
C2×#190987862
C2×#190987272
C2×#190987212
C2×#190986712
C2×#190985652
C22×#145790862
C2×#435×C792
C2×#331679